Question

If the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression…
A) has equal numerator and denominator
B) becomes a whole number
C) does not terminate
D) terminates

Answer 1

Hint: Terminating Decimal: A terminating decimal is usually defined as a decimal number that contains a finite number of digits after the decimal point.

Complete step-by-step answer:
If x is a rational number whose simplest form is $\dfrac{p}{q}$, where p and q are integers and $q \neq 0$. Then,
(i) x is terminating only when q is of the form $(2^m \times 5^n)$ for some non-negative integers m and n.
(ii) x is non-terminating and repeating, if $q \neq (2^m \times 5^n)$.
Since the denominator of given fraction has only factors of 2 and factors of 5, i.e. denominator is of the form $(2^m \times 5^n)$, thus, the given fraction terminates.
Hence, option D is correct.

Note: In this type of questions, we just check whether the prime factorization of the denominator of the fraction has only factors of 2 and 5. If it has only factors of 2 and 5, we can conclude that it is a terminating decimal.